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This paper presents a hybridized formulation for the weak Galerkin mixed finite element method (WG-MFEM) which was introduced and analyzed for second order elliptic equations. The WG-MFEM method was designed by using discontinuous piecewise…
A methodology for computing expansion basis functions using discrete harmonic modes is presented. The discrete harmonic modes are determined grain-by-grain for virtual polycrystals for which finite element meshes are available. The…
This work describes a concise algorithm for the generation of triangular meshes with the help of standard adaptive finite element methods. We demonstrate that a generic adaptive finite element solver can be repurposed into a triangular mesh…
Granular systems are not always homogeneous and can be composed of grains with very different mechanical properties. To improve our understanding of the behavior of real granular systems, in this experimental study, we compress 2D…
This article investigates parameter estimation of affine term structure models by means of the generalized method of moments. Exact moments of the affine latent process as well as of the yields are obtained by using results derived for…
We report significantly improved accuracy of grain boundary segmentation using Convolutional Neural Networks (CNN) trained on a combination of real and generated data. Manual segmentation is accurate but time-consuming, and existing…
In this paper, we introduce and analyze a lowest-order locking-free weak Galerkin (WG) finite element scheme for the grad-div formulation of linear elasticity problems. The scheme uses linear functions in the interior of mesh elements and…
Four different finite element level-set (FE-LS) formulations are compared for the modeling of grain growth in the context of polycrystalline structures and, moreover, two of them are presented for the first time using anisotropic grain…
We demonstrate how micromagnetic simulations can be employed in order to characterize and analyze the magnetic microstructure of nanocomposites. For the example of nanocrystalline Nd$-$Fe$-$B, which is a potential material for future…
Bone serves as a remarkable example of nature's architectured material with its unique blend of strength and toughness, all at a lightweight design. Given the hierarchical nature of these materials, it is essential to understand the…
Magnetoelectric effect is a fundamental physics phenomenon that synergizes electric and magnetic degrees of freedom to generate distinct material responses like electrically tuned magnetism, which serves as a key foundation of the emerging…
In this paper, we propose a multiscale empirical interpolation method for solving nonlinear multiscale partial differential equations. The proposed method combines empirical interpolation techniques and local multiscale methods, such as the…
We present here the preliminary results obtained for two experiments on randomly agitated granular assemblies using a novel way of shaking. First we discuss the transport properties of a 2D model system undergoing classical shaking that…
This paper addresses the problem of evaluating the quality of finite element meshes for the purpose of structural mechanic simulations. It proposes the application of a machine learning model trained on data collected from expert…
The millimeter wave all-metallic accelerating structure, aimed to provide more than 100 MeV/m gradient and fed by feeding RF pulses of 20-30 ns duration, is proposed. The structure is based on a waveguide with small helical corrugation.…
This paper introduces a new weak Galerkin (WG) finite element method for second order elliptic equations on polytopal meshes. This method, called WG-FEM, is designed by using a discrete weak gradient operator applied to discontinuous…
Machine learning was utilized to efficiently boost the development of soft magnetic materials. The design process includes building a database composed of published experimental results, applying machine learning methods on the database,…
We present Materium: an autoregressive transformer for generating crystal structures that converts 3D material representations into token sequences. These sequences include elements with oxidation states, fractional coordinates and lattice…
In this paper, we investigate and design multiscale simulations for stochastic multiscale PDEs. As for the space, we consider a coarse grid and a known multiscale method, the Generalized Multiscale Finite Element Method (GMsFEM). In order…
This study addresses microstructure selection mechanisms in rapid solidification, specifically targeting the transition from cellular/dendritic to planar interface morphologies under conditions relevant to additive manufacturing. We use a…